Mordred

putting these here as a visual aid to fill the GR and stress energy tensor \[\frac{dx^\alpha}{dy^{\mu}}=\frac{dx^\beta}{dy^{\nu}}=\begin{pmatrix}\frac{dx^0}{dy^0}&\frac{dx^1}{dy^0}&\frac{dx^2}{dy^0}&\frac{dx^3}{dy^0}\\\frac{dx^0}{dy^1}&\frac{dx^1}{dy^1}&\frac{dx^2}{dy^1}&\frac{dx^3}{dy^1}\\\frac{dx^0}{dy^2}&\frac{dx^1}{dy^2}&\frac{dx^2}{dy^2}&\frac{dx^3}{dy^2}\\\frac{dx^0}{dy^3}&\frac{dx^1}{dy^3}&\frac{dx^2}{dy^3}&\frac{dx^3}{dy^3}\end{pmatrix}\] Schwartzchild metric Vacuum solution [latex]T_{ab}=0[/latex] which corresponds to an unaccelerated freefall frame [latex]G_{ab}=dx^adx^b[/latex] if [latex]ds^2> 0[/latex] =spacelike propertime= [latex]\sqrt{ds^2}[/latex] [latex]ds^2<0[/latex] timelike =[latex]\sqrt{-ds^2}[/latex] [latex] ds^2=0[/latex] null=lightcone spherical polar coordinates [latex](x^0,x^1,x^2,x^3)=(\tau,r,\theta,\phi)[/latex] [latex] G_{a,b} =\begin{pmatrix}-1+\frac{2M}{r}& 0 & 0& 0 \\ 0 &1+\frac{2M}{r}^{-1}& 0 & 0 \\0 & 0& r^2 & 0 \\0 & 0 &0& r^2sin^2\theta\end{pmatrix}[/latex] line element [latex]ds^2=-(1-\frac{2M}{r}dt)^2+(1-\frac{2M}{r})^{-1}+dr^2+r^2(d \phi^2 sin^2\phi d\theta^2)[/latex] Dust solution no force acting upon particle [latex] T^{\mu\nu}=\rho_0\mu^\mu\nu^\mu[/latex] [latex]T^{\mu\nu}x=\rho_0(x)\mu^\mu(x)\mu^\nu(x)[/latex] Rho is proper matter density Four velocity [latex]\mu^\mu=\frac{1}{c}\frac{dx^\mu}{d\tau}[/latex] Leads to [latex]ds^2=-c^2d\tau^2=-c^2dt^2+dx^2+dy^2+dz^2=-c^2dt^2(1-\frac{v^2}{c^2})^\frac{1}{2}=\frac{1}{\gamma}[/latex] [latex]T^{00}=\rho_0(\frac{dt}{d\tau})^2=\gamma^2\rho_0=\rho[/latex] [latex]\rho[/latex] is mass density in moving frame. [latex]T^{0i}=\rho_0\mu^o\mu^i=\rho^o\frac{1}{c^2}\frac{dx^o}{d\tau}\frac{dx^2}{d\tau}=\gamma^2\rho_0\frac{\nu^i}{c}=\rho\frac{\nu^i}{c}[/latex] [latex]\nu^i=\frac{dx^i}{dt}[/latex] [latex]T^{ik}=\rho_0\frac{1}{c^2}\frac{dx^i}{d\tau}\frac{dx^k}{d\tau}=\gamma^2\rho\frac{\nu^i\nu^k}{c^2}=\rho\frac{\nu^i\nu^k}{c^2}[/latex] Thus [latex]T^{\mu\nu}=\begin{pmatrix}1 & \frac{\nu_x}{c}&\frac{\nu_y}{c} &\frac{\nu_z}{c} \\\frac{\nu_x}{c}& \frac{\nu_x^2}{c} & \frac{\nu_x\nu_y}{c^2}& \frac{\nu_x\nu_z}{c^2}\\ \frac{\nu_y}{c}& \frac{\nu_y\nu_z}{c^2} & \frac{\nu_y^2}{c^2}& \frac{\nu_y\nu_z}{c^2}\\ \frac{\nu_z}{c} &\frac{\nu_z\nu_x}{c^2}&\frac{\nu_z\nu_y}{c^2}&\frac{\nu_z}{c^2}\end{pmatrix}[/latex] Schwartzchild metric Vacuum solution [latex]T_{ab}=0[/latex] which corresponds to an unaccelerated freefall frame [latex]G_{ab}=dx^adx^b[/latex] if [latex]ds^2> 0[/latex] =spacelike propertime= [latex]\sqrt{ds^2}[/latex] [latex]ds^2<0[/latex] timelike =[latex]\sqrt{-ds^2}[/latex] [latex] ds^2=0[/latex] null=lightcone spherical polar coordinates [latex](x^0,x^1,x^2,x^3)=(\tau,r,\theta,\phi)[/latex] [latex] G_{a,b} =\begin{pmatrix}-1+\frac{2M}{r}& 0 & 0& 0 \\ 0 &1+\frac{2M}{r}^{-1}& 0 & 0 \\0 & 0& r^2 & 0 \\0 & 0 &0& r^2sin^2\theta\end{pmatrix}[/latex] line element [latex]ds^2=-(1-\frac{2M}{r}dt)^2+(1-\frac{2M}{r})^{-1}+dr^2+r^2(d \phi^2 sin^2\phi d\theta^2)[/latex] the above will not work directly but it is informative and will be helpful in a solution development. We will require additional terms I do know of one example that I have yet to add (the above has no acceleration for starters so this will involve rotations likely via rapidity.)

@joigusUsing the Schwartzchild solution as your basis is a good methodology for the sea level observer however be aware that to observe the clock on the orbital you will require the energy momentum terms in the T^{oi} and the T^{oj} directions. This will be further complicated in the Schwartzchild treatment as the radius to either the sea level clock and the observer at infinity will vary. I would further suggest using proper acceleration along with rapidity for the orbiting clock. I may have an appropriate solution for the orbiting clock but will have to dig it up later today

yes protons are composite particles so are neutrons I'm referring to the elementary particles that have no internal structure any composie particle would be incredibly short lived due to the high density and resulting scattering

Think of the first state as a quark gluon plasma state. Electrons neutrinos etc are present including the entirety of the standard model of particles. The energy density equates to 10^{90} photons but that's simply a calculated equivalency. That quantity is conserved throughout the expansion history though as mentioned is simply an equivalency not the actual number of photons. As mentioned they are in a state of thermal equilibrium so they all become indistinct from photons. When the electroweak symmetry break occurs then the other particles start to become distinct into neutrinos, electrons etc. Atoms come much much later.

The ASPIC library has narrowed down the number of viable inflationary models to 74 lol

neither inflation nor expansion create particles, expansion and inflation occur due to particle interactions. With inflation the two leading hypothesis for inflation is the quasi particle inflaton or the Higgs field. Both are viable though I don't believe anyone has ever observed an inflaton so in my own opinion I tend to favor the Higgs field. However that's only my opinion both are equally mathematically viable. The particles already exist in a state called thermal equilibrium in that state they are extremely short lived and highly energetic making them indistinct from one another until they drop out of thermal equilibrium. This occurs during symmetry breaking a subject that I have two threads currently active examining the related mathematics. One I have in speculation simply because some of the formulas are not typically found in textbooks but are proposed formulas from other peer review material. By thee rules of the forum I could readily consider them sufficient for mainstream but chose the Speculation forum simply to help avid confusion to other readers. (assuming they can follow the math, as I didn't include much in the way of explanation) Anyways both the inflaton field and the Higgs field incorporate the same Mexican hat potential, the potential energy at the top of the Mexican hat potential is the initial energy density. Inflation starts when the energy density starts a slow roll to the lower energy density we have today. The higher potential is oft refered to as the false vacuum. While its believed the true vacuum state we have today. The Inflation thread I have is currently in this forum for further detail. https://www.scienceforums.net/topic/128412-musings-of-a-mad-scientist-inflation-as-cosmological-constant/ this thread here has some of the mathematics I've been examining for both electroweak symmetry breaking and inflation I've been examining the slow roll itself as each stage should result in variations of the slow roll due to phase transitions. I'm still gathering the related formulas to put it all together so its layout is as I find the needed formulas lol so don't expect a clear cut order

No they certainly don't under asymptotic freedom lol.

if there is any measurable deviation in the quark sea for the valence quarks alignment it would be extremely subtle I would think likely following a probability distribution naturally. A rotating charged particle generates a magnetic moment so here is one study of precision tests of a protons magnetic moment for examination. https://arxiv.org/pdf/1201.3038.pdf edit I should reword that to any particle with an angular momentum and a charge distribution term to avoid visualization of a spinning ball oops almost forgot there is a difference in the types of magnetic moments the proton uses the nuclear magnetic moment where as the electron applies the orbital magnetic moment the proton magnetic moment is subsequently lower than the the electron magnetic moment.

well as I stated the OP never specified the quantity of protons added so I didn't assume a quantity slight correction here as protons don't generate pressure. Replace it with the curvature term however in other cases one also applies the pressure term as is the case with radiation. little FYI for everyone at the 10-{-43 sec} the mass density far exceeded the critical density which with femionic matter would have caused an instant collapse. However the system was also extremely hot and in thermal equilibrium where all particle species was so energetic to be relativistic. This lead to the negative pressure term that caused the initial expansion to get to the symmetry breaking contributions leading to inflation. Inflation regarded as either due to inflaton or Higgs inflation the effective equations of state are identical in both cases. for further clarity as I lost count on the number of people I've seen apply e=mc^2 for mass or energy and get incorrect results the full equation that would be needed to apply in this situation is the energy momentum relation \[E^2=(pc)^2+(m_0 c^2)^2\]

that depends on the effective equation of state w=0 and the critical density if you add enough protons in a small enough volume you can readily get a collapse the calculated value I got assuming no previous rate of expansion with H=0 is \[1.6-8*10^26 kg/meter\] that would be the critical density value without if you add precisely that amount the universe geometry would be perfectly Euclidean and hence static. However if you add less then the system expands and vise versa if the amount exceeds the critical density you will get a collapse. that is incorrect expansion is not purely gravitational if it were every system would collapse under self gravity you need to apply the equations of state for each particle species (radiation, matter Lambda to the fluid equations which entail the deceleration/acceleration equation of the FLRW metric which incorporate the thermodynamic contributions each particle species has

yes but as I mentioned you an also have a system of particles that collapse under self gravity. why not if your applying their effective equation of state as per the FLRW metric

The sistuation is a bit more complicated, the system of added particles may also collapse. As protons are used in the example the equation of state is w=0 which means they generate no pressure term. However matter can cause expansion but it can also collapse under self gravity. the way to determine what will happen will depend on the mass density of the added protons compared to the critical density whose value is derived via matter particles with the same equation of state. \[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\]

Hi and welcome to the forum. Well first off proving or disproving any theory in physics involves mathematics. If the theory cannot be described mathematically then it's not a theory that cannot make testable predictions. You may not be aware that a string in String theory takes a point like particle that represents its quantum properties via the string where the string is a mathematical representation of how that property behaves. How the endpoints relate to the x axis for example represent charge. Each quantum particle property has a subsequent representation of said string that is additionally mathematically described. So the first question is can you mathematically describe a single string to encompass the entirety of the standard model of particles let alone the periodic table ? Including the principle properties of said particles and atoms ? It must be able to help understand how those properties correlate to examination.

Merry Christmas hope everyone has a wonderful joyous day

Yes that example is mathematically described a parallel transport of two vectors, which returns the scalar value for the separation distance described by \[\xi\]. This parallel transport is equally used to define the various curvature terms. if the two parallel paths converge you have positive curvature. If they diverge then negative curvature. If they remain flat Euclidean geometry is preserved including those applicable to Pythagoras theorem. Angles as mentioned add up to 180 degrees. Using Barbera Rydens method you can see the relations here. http://cosmology101.wikidot.com/geometry-flrw-metric/ http://cosmology101.wikidot.com/universe-geometry is the first page of the article but the second page given prior is the one showing the universe geometry metrics

I would have to say that's an accurate short answer

ah the influence of the scale factor under commoving coordinates. Good link by the way

that's more accurate +1 in point of detail the flat universe geometry is extremely Newtonian albeit expanding. The metric is simply Euclidean with the scale factor representing the commoving coordinate changes (for the Flat Euclidean case)

As mentioned by Swansont further detail is needed. However first off I recommend you forget any imagery of particles as little bullets as your descriptive seems to apply. You are correct in so far as certain particles do interact more readily with other particles however your solution makes little to no sense. mass is resistance to inertia change or acceleration it results in a particles via the particles ability to couple with its respective fields. This includes the Higgs field. To examine how mass arises as a result of the Higgs field you can apply the Weinberg angles of the CKMS matrix using the particles cross section.

apply Newtons shell theorem a uniform mass distribution wouldn't have gravity as you wouldn't have any net force at any arbitrary coordinate treated as center of mass. Gravity itself requires non uniformity of mass distribution

Not precisely Newton physics also includes the Newton Shell theorem. In that shell theorem a uniform mass distribution would have no gravity. However if you have an anisotropic distribution such as the the Earth where gravity is weak we don't have significant time dilation effects. so the Newton method for everyday measurements are still accurate. It is only when you get extremely fine tuned in your examination that the time dilation becomes measurable. so there is curvature aka gravity but the curvature isn't significant and we can still get good approximation under Euclidean flat geometry. Ok lets take two falling objects you can do this with a pen and paper easily enough Draw a circle. the Center of the circle is your center of mass. Choose two angles from that center of mass say 15 degrees and 345 degrees. Let those represent the two infalling particles toward the CoM. You assign a variable to represent the separation distance between the two infalling particles at a given radius. The common symbol used is \[\xi\] the value will decrease as the particles approach the CoM. this is termed tidal force due to the geometry (curved spacetime though under Euclidean approximation ) this is often described as gravity as the tidal force due to curved spacetime

Under GR through the Principle of General Covariance it would be represented under the Newton approximation solutions of the Einstein field equations. The simplest transform is the Minkowskii metric, Euclidean space or flat space. This is denoted by [latex]\eta[[/latex] [latex]\mathbb{R}^4 [/latex] with Coordinates (t,x,y,z) or alternatively (ct,x,y,z) flat space is done in Cartesian coordinates. In this metric space time is defined as [latex] ds^2=-c^2dt^2+dx^2+dy^2+dz^2=\eta_{\mu\nu}dx^{\mu}dx^{\nu}[/latex] [latex]\eta=\begin{pmatrix}-c^2&0&0&0\\0&1&0&0\\0&0&1&0\\0&0&0&1\end{pmatrix}[/latex] the metric above works well to describe The Newton limit provided provided you don't have significant relativity effects due to either inertia or extreme mass. Though these equations do describe the essentials of SR, they still readily apply for situations not involving gamma of the Lorentz transforms.

My interest in Cosmology started back in the late 70's. However in the early 80's when Alllen Guth's first published his false vacuum inflation model accelerated that interest even further. That interest has been a primary focus of my studies ever since. Back then inflation often involved quantum tunnelling from a false vacuum state to a true vacuum state. These models typically had the energy density graph transitions as in a similar fashion to https://www.wolframalpha.com/input?i2d=true&i=plot+Power[x%2C2] thoough they would often include a higher potential of the same curve to represent the stable region of the higher potential false vacuum state. Those graphs then were employed to define quantum tunneling from the two potential VeV's through the separation potential barrier between their corresponding stable regions. Modern models however use the Mexican hat potential as per the inflaton and the Higgs field. Their effective equations of state are close matches. Today there is strong supportive evidence that Higgs inflation is highly viable. However the inflaton is also equally viable. The latter includes chaotic eternal inflation leading to pocket multiverses defined by separate expansion regions with the causal connection of the same inflation mechanism that rapidly expanded our universe in early times. I had also had to ask myself the question. Is there a connection between inflation and the cosmological constant ? " given the behavior of inflation I found that this is highly likely. I will support this with the relevant equations however it will take time to place them into the thread. ( I will be saving often during edits)So starting from our hot dense state at 10^{-43} seconds. (prior to this leads to infinite blueshift as well as other infinity problems. ( The Big Bang mathematical singularity conditions) so first we need our metric LCDM FLRW Metric equations \[d{s^2}=-{c^2}d{t^2}+a({t^2})[d{r^2}+{S,k}{(r)^2}d\Omega^2]\] \[S\kappa(r)= \begin{cases} R sin(r/R &(k=+1)\\ r &(k=0)\\ R sin(r/R) &(k=-1) \end {cases}\] \[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\] \[H^2=(\frac{\dot{a}}{a})^2=\frac{8 \pi G}{3}\rho+\frac{\Lambda}{3}-\frac{k}{a^2}\] setting \[T^{\mu\nu}_\nu=0\] gives the energy stress mometum tensor as \[T^{\mu\nu}=pg^{\mu\nu}+(p=\rho)U^\mu U^\nu)\] \[T^{\mu\nu}_\nu\sim\frac{d}{dt}(\rho a^3)+p(\frac{d}{dt}(a^3)=0\] which describes the conservation of energy of a perfect fluid in commoving coordinates describes by the scale factor a with curvature term K=0. the related GR solution the the above will be the Newton approximation. \[G_{\mu\nu}=\eta_{\mu\nu}+H_{\mu\nu}=\eta_{\mu\nu}dx^{\mu}dx^{\nu}\] Thermodynamics Tds=DU+pDV Adiabatic and isentropic fluid (closed system) equation of state \[w=\frac{\rho}{p}\sim p=\omega\rho\] \[\frac{d}{d}(\rho a^3)=-p\frac{d}{dt}(a^3)=-3H\omega(\rho a^3)\] as radiation equation of state is \[p_R=\rho_R/3\equiv \omega=1/3 \] radiation density in thermal equilibrium is therefore \[\rho_R=\frac{\pi^2}{30}{g_{*S}=\sum_{i=bosons}gi(\frac{T_i}{T})^3+\frac{7}{8}\sum_{i=fermions}gi(\frac{T_i}{T})}^3 \] \[S=\frac{2\pi^2}{45}g_{*s}(at)^3=constant\] temperature scales inversely to the scale factor giving \[T=T_O(1+z)\] with the density evolution of radiation, matter and Lambda given as a function of z \[H_z=H_o\sqrt{\Omega_m(1+z)^3+\Omega_{rad}(1+z)^4+\Omega_{\Lambda}}\] the above typically has the equation of states cosmology given by https://en.wikipedia.org/wiki/Equation_of_state_(cosmology) where the scalar field is the given equation of state for the cosmological constant. \[w=\frac{\frac{1}{2}V\dot{\varphi^2}-V(\varphi)}{\frac{1}{2}V\dot{\varphi^2}+V(\varphi)}\] Higgs Inflation Single scalar field Modelling. \[S=\int d^4x\sqrt{-g}\mathcal{L}(\Phi^i\nabla_\mu \Phi^i)\] g is determinant Einstein Hilbert action in the absence of matter. \[S_H=\frac{M_{pl}^2}{2}\int d^4 x\sqrt{-g\mathbb{R}}\] set spin zero inflaton as \[\varphi\] minimally coupled Langrangian as per General Covariance in canonical form. (kinetic term) \[\mathcal{L_\varphi}=-\frac{1}{2}g^{\mu\nu}\nabla_\mu \varphi \nabla_\nu \varphi-V(\varphi)\] where \[V(\varphi)\] is the potential term integrate the two actions of the previous two equations for minimal scalar field gravitational couplings \[S=\int d^4 x\sqrt{-g}[\frac{M_{pl}^2}{2}\mathbb{R}-\frac{1}{2}g^{\mu\nu}\nabla_\mu\varphi \nabla_\nu \varphi-V(\varphi)]\] variations yield the Euler_Langrene \[\frac{\partial \mathcal{L}}{\partial \Phi^i}-\nabla_\mu(\frac{\partial \mathcal{L}}{\partial[\nabla_\mu \Phi^i]})=0\] using Euclidean commoving metric \[ds^2-dt^2+a^2(t)(dx^2+dy^2=dz^2)\] this becomes \[\ddot{\varphi}+3\dot{\varphi}+V_\varphi=0\] \[S=\int d^4 x\sqrt{-g}[\frac{M_{pl}^2}{2}\mathbb{R}-\frac{1}{2}g^{\mu\nu}\nabla_\mu\varphi \nabla_\nu \varphi-V(\varphi)]\] and \[G_{\mu\nu}-\frac{1}{M_{pl}}T_{\mu\nu}\] with flat commoving geometry of a perfect fluid gives the energy momentum for inflation as \[T^\mu_\nu=g^{\mu\lambda}\varphi_\lambda \varphi_\nu -\delta^\mu_\nu \frac{1}{2}g^{\rho \sigma} \varphi_\rho \varphi_\sigma V(\varphi)]\] \[\rho=T^0_0=\frac{1}{2}\dot{\varphi}^2+V\] \[p=T^i_i (diag)=\frac{1}{2}\dot{\varphi}^2-V\] \[w=\frac{p}{\rho}\] \[w=\frac{1-2 V/\dot{\varphi^2}}{1+2V/\dot{\varphi^2}}\] ***method by Fernando A. Bracho Blok Thesis paper.*** https://helda.helsinki.fi/bitstream/handle/10138/322422/Brachoblok_fernando_thesis_2020.pdf?sequence=2&isAllowed=y Now any scalar field state dominated by the potential energy density will have negative pressure. a negative pressure to energy density ratio of w=-1 will describe a state that does not vary over time. However this also involves the critical density. \[\rho_{crit} = \frac{3c^2H^2}{8\pi G}\] the initial conditions will have a different critical density value at the false vacuum state prior to inflation. A critically dense universe is a k=0 flat universe. However it derivatives employ a pressure less w=0 equation of state to derive the critical density value. This corresponds to the equation of state for matter. in essence the universe is thermodynamically evolving from a hot dense state of a negative vacuum with opposing force relations given by replacement \[\rho_{(V\varphi)}\] to \[V(\phi) \[DU=\rho_{V(\phi)}DV\] work is defined as \[dW=\rho_{V(\phi)}dV\] \[p_{V(\phi)}=-\rho_{V(\phi)}\] the slower the roll from false vacuum potential to VeV today allows for greater number of e-folds. The greater the e-fold ratio the higher the number of pocket universes that can result in locally anisotropic regions during inflation. Examinations under the eternal chaotic inflationary theory can lead up to an infinite amount of bubble or pocket universes. This arises with the result of a locally different rate in inflation to the global rate. Once inflation slow rolls the VeV reduces on a gradual but not necessarily smooth rate, smaller metastable states arise due to thermal dropout of particle species as well as base elements such as hydrogen and lithium. The expansion and Cosmological redshift following the thermodynamic laws also contribute to the evolution to the scale factor. I will add further detail later on (long work day)

Higgs Inflation Single scalar field Modelling. \[S=\int d^4x\sqrt{-g}\mathcal{L}(\Phi^i\nabla_\mu \Phi^i)\] g is determinant Einstein Hilbert action in the absence of matter. \[S_H=\frac{M_{pl}^2}{2}\int d^4 x\sqrt{-g\mathbb{R}}\] set spin zero inflaton as \[\varphi\] minimally coupled Langrangian as per General Covariance in canonical form. (kinetic term) \[\mathcal{L_\varphi}=-\frac{1}{2}g^{\mu\nu}\nabla_\mu \varphi \nabla_\nu \varphi-V(\varphi)\] where \[V(\varphi)\] is the potential term integrate the two actions of the previous two equations for minimal scalar field gravitational couplings \[S=\int d^4 x\sqrt{-g}[\frac{M_{pl}^2}{2}\mathbb{R}-\frac{1}{2}g^{\mu\nu}\nabla_\mu\varphi \nabla_\nu \varphi-V(\varphi)]\] variations yield the Euler_Langrene \[\frac{\partial \mathcal{L}}{\partial \Phi^i}-\nabla_\mu(\frac{\partial \mathcal{L}}{\partial[\nabla_\mu \Phi^i]})=0\] using Euclidean commoving metric \[ds^2-dt^2+a^2(t)(dx^2+dy^2=dz^2)\] this becomes \[\ddot{\varphi}+3\dot{\varphi}+V_\varphi=0\] \[S=\int d^4 x\sqrt{-g}[\frac{M_{pl}^2}{2}\mathbb{R}-\frac{1}{2}g^{\mu\nu}\nabla_\mu\varphi \nabla_\nu \varphi-V(\varphi)]\] and \[G_{\mu\nu}-\frac{1}{M_{pl}}T_{\mu\nu}\] with flat commoving geometry of a perfect fluid gives the energy momentum for inflation as \[T^\mu_\nu=g^{\mu\lambda}\varphi_\lambda \varphi_\nu -\delta^\mu_\nu \frac{1}{2}g^{\rho \sigma} \varphi_\rho \varphi_\sigma V(\varphi)]\] \[\rho=T^0_0=\frac{1}{2}\dot{\varphi}^2+V\] \[p=T^i_i (diag)=\frac{1}{2}\dot{\varphi}^2-V\] \[w=\frac{p}{\rho}\] \[w=\frac{1-2 V/\dot{\varphi^2}}{1+2V/\dot{\varphi^2}}\] ***method by Fernando A. Bracho Blok Thesis paper.*** https://helda.helsinki.fi/bitstream/handle/10138/322422/Brachoblok_fernando_thesis_2020.pdf?sequence=2&isAllowed=y now to examine it to other Higgs single scalar field field methodologies. in particular https://arxiv.org/abs/1402.3738 equation 16 of the above article matches 2.38 and 2.39 of the Brachoblok paper with two different methodologies. (cool need to further study both methods) \[\rho=T^0_0=\frac{1}{2}\dot{\varphi}^2+V\] \[p=T^i_i (diag)=\frac{1}{2}\dot{\varphi}^2-V\] https://arxiv.org/abs/1303.3787 (for this I will need to research Jordon frame) in particular page 23 (single scalar Higgs) goals check list. (single scalar field (Higgs prior to electroweak symmetry breakings. For symmetry break (Higgs and Yukawa couplings of the CkMS unity triangle.). Follow through with each particle species including generations via Higgs). (details and preliminary work aforementioned). Hydrogen, lithium and deuterium dropout. (Saha equations) for particle species Maxwell Boltzmann, Bose-Einstein and Fermi Dirac. statistics). Apply Principle of General Covariance throughout.

To add to Phi for All's excellent reply time is simply ratevof change. It is given dimensionality equivalence to length via the interval defined as (ct). Spacetime is simply the geometry where particles reside. Space being simply the volume.